An accurate molecular mechanics model for computation of size-dependent elastic properties of armchair and zigzag single-walled carbon nanotubes

In this paper, an analytical solution based on a molecular mechanics model is developed to evaluate the mechanical properties of armchair and zigzag single-walled carbon nanotubes (SWCNTs). Adopting the Perdew–Burke–Ernzerhof (PBE) exchange correlation, the density functional theory (DFT) calculations are performed within the generalized gradient approximation (GGA) to evaluate force constants used in the molecular mechanics model. After that, based on the principle of molecular mechanics, explicit expressions are proposed to obtain surface Young’s modulus, Poisson’s ratio and surface shear modulus of SWCNTs corresponding to both types of armchair and zigzag chiralities. Based on the DFT calculations, it is found that the flexural rigidity of graphene is independent of the type of chirality which indicates the isotropic characteristic of this material. Moreover, it is observed that for the all values of nanotube diameter, surface Young’s modulus for the armchair nanotube is more than that of zigzag nanotube. It is shown that the trend predicted by the present model is in good agreement with other models which confirms the validity as well as the accuracy of the present molecular mechanics model.